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Gas diffusion behavior in fractal porous media is simulated by Monte Carlo technique in this work. Based on the fractal character of pore size in porous media, the probability model of the effective gas diffusion coefficient is derived. The proposed model of the effective gas diffusion coefficient is explicitly expressed as a function of structural parameters of porous media, such as porosity, pore size, the fractal dimensions for pore area and tortuosity. The effect of structural parameters of porous media has been studied in detail. The results show that the present results from the Monte Carlo simulations present a good agreement with those from the available analytical model and the available experimental data. The proposed Monte Carlo simulation technique may have the potential in predictions of other gas transport properties in fractal porous media.

Understanding gas transport behavior though fractured porous media is essential in many fields including fiber science, energy science, soil science, environmental engineering, chemical engineering, etc. In this paper, a fractal model is developed to characterize gas diffusion through fractured porous media, where a bundle of fractal-like tree branching networks is used to represent the fracture system according to fractal scaling laws. The analytical expression for relative gas diffusion coefficient of fractured porous media is derived. The proposed fractal model has been validated by the available experimental data and empirical correlations. From the parametrical study, it can be seen that structural parameters of fractured porous media (for example porosity, the fractal dimension, the diameter ratio, the length ratio and the branching angle) have a significant effect on equivalent gas transport properties. Gas relative diffusion coefficient has a positive correlation with the porosity, the pore size fractal dimension, or the diameter ratio, whereas it has a negative correlation with the length ratio, the branching levels, or the branching angle. The proposed fractal model does not only shed light on gas transport physics of fractured porous media, but also reveals more mechanisms than experimental measurements.

Fractal model of gas diffusion through porous fibrous materials with rough surfaces is derived, in which the porous structure is simplified to be composed of a bundle of tortuous capillaries whose pore size distribution and surface roughness follow the fractal scaling laws. The analytical expression for gas relative diffusion coefficient is a function of the relative roughness, fiber radius and the other microstructural parameters (porosity, the fractal dimension for pore size distribution and tortuosity, the maximum and minimum pore diameter and the characteristic length). The proposed fractal model is validated by comparison with available experimental data and correlations. At the same time, the effect of microstructural parameters of porous fibrous materials on gas diffusion has been studied in detail. It is believed that the current model may be extended to porous materials other than fibrous materials.

Fractal model of gas diffusion in porous nanofibers with rough surfaces is derived, in which the porous structure is assumed to be composed of a bundle of tortuous capillaries whose pore size distribution and surface roughness follow the fractal scaling laws. The analytical expression for gas relative diffusion coefficient is a function of the relative roughness and the other microstructural parameters (porosity, the fractal dimension for pore size distribution and tortuosity, the maximum and minimum pore diameter and the characteristic length). The proposed fractal model is validated by comparison with available experimental data and correlations. At the same time, the effect of microstructural parameters of porous fibrous materials on gas diffusion has been studied in detail. It is believed that the current model may be extended to porous materials other than fibrous materials.

This work investigates the effect of surface roughness on gas diffusion behavior in the composite, which is composed of porous media embedded with a fractal-like tree network. Based on rough elements of wall surfaces of the tree network of this composite following the fractal scaling law, gas diffusion coefficient is expressed as a function of micro-structural parameters of this composite (such as the relative roughness, the porosity, the diameter ratio, the length ratio, the branching level and the branching angle). It is found that our model is more consistent with available experimental data than empirical correlations. In addition, the influence of the relative roughness and the other micro-structural parameters on gas diffusion has been analyzed. It is believed that the current model could reveal more physical mechanisms than empirical models.

Gas diffusion coefficient is an important parameter in characterizing gas transport in porous media. Based on the fractal characteristics of microscopic capillaries, the effect of capillary surface roughness on gas diffusion is considered by the Monte Carlo technique. We proposed a probability model of the effective gas diffusion coefficient of the porous media with rough surfaces. This model is expressed as a function of the geometrical parameters of porous media, such as the porosity, the pore fractal dimension, the tortuosity fractal dimension, and the relative roughness. The simulated effective gas diffusion coefficient is compared with the available experimental data and a good agreement between them is obtained. The effect of the structural parameters of porous media on gas diffusion is analyzed in detail.

A novel gas diffusivity model for dry porous media with a damaged tree-like branching network is proposed by using the fractal theory in this study. We systematically investigated the effects of the number of damaged channels and the other structural parameters on the dimensionless gas diffusivity (DGD) and concentration drop. As the number of damaged channels increases, the DGD presents a decreasing trend, while the ratio of concentration drop shows a rising tendency. Meanwhile, the DGD is negatively correlated to the length exponent, the total number of branching levels, and the branching angle, respectively. On the other hand, the DGD is positively correlated with the diameter exponent. Besides, the ratio of concentration drop is negatively correlated with the length exponent and the total number of branching levels. However, it is positively associated with the diameter exponent and branching levels. In addition, during the calculation of the value of concentration drop, the total concentration drop can be disassembled into two equal-ratio sequences. And the scale factors in sequences are constants that are independent of the number of damaged channels. The reliability of the model predictions was verified by a comparison with the experimental data available in the literature. The physical mechanism of gas diffusion in the damaged network may be well explained by the proposed model.